Integral representations of the Riemann zeta function of odd argument

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Pain, Jean-Christophe
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866910678447554560
author Pain, Jean-Christophe
author_facet Pain, Jean-Christophe
contents In this article we obtain, using an expression of the digamma function $ψ(x)$ due to Mikolas, integral representations of the zeta function of odd arguments $ζ(2p+1)$ for any positive value of $p$. The integrand consists of the product of a polynomial by one or two elementary trigonometric functions. Examples for the first values of the argument are given. Some of them were already derived by other methods.
format Preprint
id arxiv_https___arxiv_org_abs_2410_23096
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Integral representations of the Riemann zeta function of odd argument
Pain, Jean-Christophe
Number Theory
In this article we obtain, using an expression of the digamma function $ψ(x)$ due to Mikolas, integral representations of the zeta function of odd arguments $ζ(2p+1)$ for any positive value of $p$. The integrand consists of the product of a polynomial by one or two elementary trigonometric functions. Examples for the first values of the argument are given. Some of them were already derived by other methods.
title Integral representations of the Riemann zeta function of odd argument
topic Number Theory
url https://arxiv.org/abs/2410.23096